雷大江^1,,,
唐建烊¹,
李智星¹,
吴渝²
1.重庆邮电大学计算机科学与技术学院 重庆 400065
2.重庆邮电大学网络智能研究所 重庆 400065
基金项目:重庆市留学归国人员创新创业项目支持人选(cx2018120)，国家社会科学基金(17XFX013)，重庆市基础研究与前沿探索项目(cstc2015jcyjA40018)

详细信息

作者简介:雷大江：男，1979年生，副教授，研究方向为机器学习
唐建烊：男，1993年生，硕士生，研究方向为核机器学习
李智星：男，1985年生，副教授，研究方向为自然语言处理
吴渝：女，1970年生，教授，研究方向为网络智能

通讯作者:雷大江　leidj@cqupt.edu.cn

中图分类号:TN911.7; TP181

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出版历程

收稿日期:2019-06-11
修回日期:2020-03-28
网络出版日期:2020-08-27
刊出日期:2020-11-16

Sparse Multinomial Logistic Regression Algorithm Based on Centered Alignment Multiple Kernels Learning

Dajiang LEI^1,,,
Jianyang TANG¹,
Zhixing LI¹,
Yu WU²
1. College of Computer, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2. Institute of Web Intelligence, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Funds:The Chongqing Innovative Project of Overseas Study(cx2018120), The National Social Science Foundation of China(17XFX013), The Natural Science Foundation of Chongqing(cstc2015jcyjA40018)


摘要
摘要:稀疏多元逻辑回归(SMLR)作为一种广义的线性模型被广泛地应用于各种多分类任务场景中。SMLR通过将拉普拉斯先验引入多元逻辑回归(MLR)中使其解具有稀疏性，这使得该分类器可以在进行分类的过程中嵌入特征选择。为了使分类器能够解决非线性数据分类的问题，该文通过核技巧对SMLR进行核化扩充后得到了核稀疏多元逻辑回归(KSMLR)。KSMLR能够将非线性特征数据通过核函数映射到高维甚至无穷维的特征空间中，使其特征能够充分地表达并最终能进行有效的分类。此外，该文还利用了基于中心对齐的多核学习算法，通过不同的核函数对数据进行不同维度的映射，并用中心对齐相似度来灵活地选取多核学习权重系数，使得分类器具有更好的泛化能力。实验结果表明，该文提出的基于中心对齐多核学习的稀疏多元逻辑回归算法在分类的准确率指标上都优于目前常规的分类算法。
关键词:稀疏优化/
核技巧/
多核学习/
稀疏多元逻辑回归
Abstract:As a generalized linear model, Sparse Multinomial Logistic Regression (SMLR) is widely used in various multi-class task scenarios. SMLR introduces Laplace priori into Multinomial Logistic Regression (MLR) to make its solution sparse, which allows the classifier to embed feature selection in the process of classification. In order to solve the problem of non-linear data classification, Kernel Sparse Multinomial Logistic Regression (KSMLR) is obtained by kernel trick. KSMLR can map nonlinear feature data into high-dimensional and even infinite-dimensional feature spaces through kernel functions, so that its features can be fully expressed and eventually classified effectively. In addition, the multi-kernel learning algorithm based on centered alignment is used to map the data in different dimensions through different kernel functions. Then center-aligned similarity can be used to select flexibly multi-kernel learning weight coefficients, so that the classifier has better generalization ability. The experimental results show that the sparse multinomial logistic regression algorithm based on center-aligned multi-kernel learning is superior to the conventional classification algorithm in classification accuracy.
Key words:Sparse optimization/
Kernel trick/
Multiple kernels learning/
Sparse Multinomial Logistic Regression(SMLR)



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